Question

Prove that if AB= 0and A is invertible then B= 0

Answer 1

Answer with Step-by-step explanation:

Since we have given that

AB = 0 and A is invertible so, AA⁻¹ = I

So, Consider,

`AB=0`

Multiplying A⁻¹ on both the sides, we get that

`A^(-1)AB=A^(-1)0\\\\(AA^(-1))B=0\\\\IB=0\\\\B=0`

Hence proved.